Biostatistics for the biological and health sciences 2nd edition triola test bank

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Chapter 7 Exam A Name MULTIPLE CHOICE. Select the choice that best answers the problem.

1) Use the given level of confidence and statistics to construct a confidence interval for the population proportion p. n = 195, x = 162; 95% confidence A) 0.778 < p < 0.883 B) 0.788 < p < 0.873 C) 0.789 < p < 0.873 D) 0.777 < p < 0.884

1)____________

2) Find the value of zα / 2 that corresponds to a confidence level of 89.48%.

A) 1.25 B) 1.62 C) 0.0526 D) −1.62

2)____________

3) Express the confidence interval (0.432, 0.52) in the form of pˆ ± E.

3)____________

A) 0.476 ± 0.044 C) 0.432 ± 0.044 4) Find the critical value χ

B) 0.476 ± 0.088 D) 0.432 ± 0.088

2 corresponding to a sample size of 19 and a confidence level of R

4)____________

99 percent.

A) 37.156

B) 6.265

C) 34.805

D) 7.015

5) Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.

98% confidence; the sample size is 800, of which 40% are successes A) 0.0355 B) 0.0339 C) 0.0404 D) 0.0446

5)____________

6) Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over six feet tall. What is the best point estimate of the proportion of people in the population who are over 6 feet tall?

A) 0.76 B) 0.24 C) 0.50 D) 0.18

6)____________

7) Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.

A) 0.0323 < p < 0.0782 B) 0.0360 < p < 0.0745 C) 0.0251 < p < 0.0854 D) 0.0280 < p < 0.0826

7)____________

8) Use the given information to find the minimum sample size required to estimate the population proportion.

Margin of error: 0.028; confidence level: 99%; p and q unknown A) 1116 B) 2223 C) 1939 D) 2115

8)____________

9) Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

95% confidence; n = 2388, x = 1672 A) 0.0248 B) 0.0184 C) 0.0156 D) 0.0206

9)____________

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10) Use the given level of confidence and statistics to construct a confidence interval for the population mean μ . Assume that the population has a normal distribution.

10)___________

Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.

B) 91.69 < μ < 98.31 A) 91.68 < μ < 98.32 C) 92.95 < μ < 97.05

D) 92.03 < μ v < 97.97

11) A survey of 300 marine biologists reveals that 112 favor the tagging the flippers of king penguins. Construct the 98% confidence interval for the true population proportion of marine biologists that favor tagging the flippers of king penguins.

A) 0.316 < p < 0.430 B) 0.301 < p < 0.445 C) 0.308 < p < 0.438 D) 0.304 < p < 0.442

11)___________

12) Determine which is the correct distribution.

95% Confidence Interval for μ ; n = 150; s = 550 . The sample data appear to come from a normally distributed population.

A) Normal distribution B) Student t distribution C) Chi-square distribution D) None of the above

12)___________

13) Use the given level of confidence and statistics to construct a confidence interval for the population mean μ . Assume that the population has a normal distribution.

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

B) 175.9 mg < μ < 194.1 mg A) 173.7 mg < μ < 196.3 mg C) 173.8 mg < μ < 196.2 mg D) 173.9 mg < μ < 196.1 mg

13)___________

14) Which critical value is appropriate for a 99% confidence level where n = 17; σ is unknown and the population appears to be normally distributed?

A) tα /2 = 2.898 B) zα / 2 = 2.583 C) tα /2 = 2.921 D) zα / 2 = 2.567

14)___________

15) Use the given level of confidence and statistics to construct a confidence interval for the population mean μ . Assume that the population has a normal distribution. n = 30, x = 84.6, s = 10.5, 90% confidence A) 79.32 < μ < 89.88 B) 81.36 < μ < 87.84 C) 81.34 < μ < 87.86 D) 80.68 < μ < 88.52

15)___________

16) Find the critical value zα / 2 that corresponds to a 91% confidence level.

A) 1.34 B) 1.645 C) 1.70 D) 1.75

16)___________

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17) Do one of the following, as appropriate: (a) Find the critical value zα / 2 , (b) find the critical value tα / 2 , (c) state that neither the normal nor the t distribution applies.

90% confidence interval for μ; n = 9; σ = 4.2; population appears to be very skewed.

A) zα / 2 = 2.896 B) zα / 2 = 2.365 C) zα / 2 = 2.306 D) Neither the normal nor the t distribution applies.

17)___________

18) Identify the distribution that applies to the following situation: In constructing a confidence interval of σ you have 50 sample values and they appear to be from a population with a skewed distribution.

A) Student t distribution B) Normal distribution C) Chi-square distribution D) None of the three distributions is appropriate.

18)___________

19) If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n _______ (up or down) to the next ________ (smaller or larger) whole number.

A) up; smaller B) up; larger C) down; smaller D) down; larger

19)___________

20) The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.

A) increases; increases B) increases; decreases C) decreases; increases D) decreases; decreases

20)___________

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Answer Key Testname: CHAPTER 7 EXAM A 1) A 2) B 3) A 4) A 5) C 6) B 7) A 8) D 9) B 10) A 11) C 12) B 13) C 14) C 15) C 16) C 17) D 18) A 19) B 20) C

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Chapter 7 Exam B Name MULTIPLE CHOICE. Select the choice that best answers the problem.

1) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. A confidence interval of 173.8 mg < μ < 196.2 mg is constructed for the true mean cholesterol content of all such eggs. It was assumed that the population has a normal distribution. What confidence level does this interval represent?

A) 99% B) 95% C) 98% D) 80%

1)____________

2) Which of the following critical values is appropriate for a 98% confidence level where n = 7; σ = 27 and the population appears to be normally distributed.

D) tα /2 = 2.575 A) zα / 2 = 2.33 B) zα / 2 = 2.05 C) tα / 2 = 1.96

2)____________

3) To find the standard deviation of the diameter of potted Areca palm trunks, a biologist measures 19 randomly selected palms and finds the standard deviation of the sample to be s = 0.16 meters. Find the 95% confidence interval for the population standard deviation σ .

A) 0.12 < σ < 0.24 B) 0.15 < σ < 0.21 C) 0.11 < σ < 0.25 D) 0.13 < σ < 0.22

3)____________

4) A one-sided confidence interval for p can be written as p < pˆ + E or p > pˆ − E where the margin of error E is modified by replacing zα / 2 with zα . If a teacher wants to report that the fail rate on a test is at most x with 90% confidence, construct the appropriate one -sided confidence interval. Assume that a simple random sample of 74 students results in 8 who fail the test.

A) p < 0.062 B) p < 0.154 C) p > 0.062 D) p < 0.167

4)____________

5) Use the given information to find the minimum sample size required to estimate the population proportion.

Margin of error: 0.008; confidence level: 98%; p̂ and q̂ unknown A) 22,184 B) 10,384 C) 21,207 D) 20,308

5)____________

6) Use the given level of confidence and statistics data to construct a confidence interval for the population proportion p. n = 130, x = 69; 90% confidence A) 0.458 < p < 0.604 B) 0.461 < p < 0.601 C) 0.459 < p < 0.603 D) 0.463 < p < 0.599

6)____________

7) Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

A) 18.1% < p < 39.6% B) 21.9% < p < 35.7% C) 19.1% < p < 38.5% D) 20.6% < p < 37.0%

7)____________

8) A 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3.

This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation.)

B) 65.9 in. < μ < 67.1 in.

A) 65.7 in. < μ < 67.3 in.

C) 65.6 in. < μ < 67.4 in.

D) 66.0 in. < μ < 67.0 in.

8)____________

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9) A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, μ , of all students taking the test?

B) 28.4 < μ < 30.6 A) 28.2 < μ < 30.8 D) 27.9 < μ < 31.1 C) 27.8 < μ < 31.2

9)____________

10) A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with σ = 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.

B) 224 mg < μ < 232 mg A) 223 mg < μ < 232 mg C) 225 mg < μ < 233 mg D) 223 mg < μ < 231 mg

10)___________

11) Find the critical value χ

2 R

corresponding to a sample size of 19 and a confidence level of 99

11)___________

percent.

A) 37.156

B) 6.265

C) 34.805

D) 7.015

12) Use the given level of confidence and statistics to construct a confidence interval for the population proportion p. n = 56, x = 30; 95% confidence A) 0.405 < p < 0.667 B) 0.425 < p < 0.647 C) 0.426 < p < 0.646 D) 0.404 < p < 0.668

12)___________

13) Find the degree of confidence used in constructing the confidence interval 0.523 < p < 0.669 for the population proportion p using sample data with n = 109, x = 65.

A) 88% B) 90% C) 95% D) 99%

13)___________

14) You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

A) 57 B) 224 C) 14 D) 11

14)___________

15) To be able to say with 95% confidence that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what quantity?

A) 805 B) 192 C) 335 D) 250

15)___________

16) Express the confidence interval 0.039 < p < 0.479 in the form of pˆ ± E. A) 0.220 ± 0.5 B) 0.259 ± 0.22 C) 0.259 ± 0.5 D) 0.259 ± 0.44

16)___________

17) Do one of the following, as appropriate: (a) Find the critical value zα / 2 , (b) find the critical value tα /2 .

99%; n = 17; σ is unknown; population appears to be normally distributed.

B) zα /2 = 2.567 A) zα / 2 = 2.583 C) tα /2 = 2.921 D) tα /2 = 2.898

17)___________

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18) Identify the distribution that applies to the following situation: In constructing a confidence interval of µ, you have 50 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known. ______________.

A) Student t distribution B) Normal distribution C) Chi-square distribution D) None of the three distributions is appropriate.

18)___________

19) Express a confidence interval defined as (0.432, 0.52) in the form of the point estimate ___________ ± the margin of error __________. Express both to three decimal places.

A) 0.476 ± 0.044 B) 0.476 ± 0.088 C) 0.432 ± 0.088 D) 0.432 ± 0.044

19)___________

20) Fill in the blank: The critical value zα / 2 that corresponds to a _________% confidence level is 20)___________ 2.33.

A) 88 B) 90 C) 98 D) 99

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Answer Key Testname: CHAPTER 7 EXAM B 1) B 2) A 3) A 4) B 5) C 6) C 7) D 8) B 9) B 10) B 11) A 12) A 13) A 14) A 15) B 16) B 17) C 18) A 19) A 20) C

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Chapter 7 Exam C Name SHORT ANSWER. Using the following information, write the word, phrase, or value that best answers the problem.

1) Find the critical value zα / 2 that corresponds to a confidence level of 90%,

1)____________

2) Six human skulls from around 4000 B.C. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9 mm. If you want to construct a 95% confidence interval estimate of the mean length of skulls, what requirements must be satisfied?

2)____________

3) Use the following confidence level interval limits to find the point estimate p̂ and the margin of error E. An aquatic site adjacent to an old woodchipping mill is being studied to determine whether environmental liabilities exist from previous woodchipping operations. Because wood chips can leach toxic compounds into the water, environmental consultants measure the proportion of wood chips found in samples taken from various sediment cores. They find the confidence interval of the proportion of wood chips is from 0.194 to 0.228.

3)____________

For the next two questions, assume a simple random sample has been taken, the conditions for a binomial distribution are satisfied, and the sample proportions can be approximated by a normal distribution. The Department of Fish and Wildlife is interested in whether they need to modify fishing regulations on sturgeon in a certain river. From a sample of 200 sturgeon caught, the number of breeding adults was 20. Use a 95% confidence level.

4) Find the margin of error E that corresponds to the above statistics and confidence level.

4)____________

5) Use the sample data and confidence level to construct a confidence interval estimate of the

5)____________

population proportion p.

6) Find the minimum sample size required to estimate a population proportion p.

Margin of error: four percentage points; confidence level: 95%; from a prior study, p̂ is estimated by the decimal equivalent 12.5%.

6)____________

7) Use the following confidence level interval limits to find the point estimate x and the margin of error E. Medical researchers, studying the improvement of individuals with Down Syndrome on a language and memory test after taking a certain drug, find the confidence interval of the mean test score improvement to be from 13.96 to 16.04.

7)____________

For the next two questions, assume a simple random sample has been taken, the population standard deviation is known, and the population is normally distributed. According to a sample of 200 various insurance brokers and health experts, a typical childbirth in the United States costs a mean of $9500. Assume we know from a previous study, the standard deviation of the cost of the births is $2500. Use a 98% confidence level.

8) Find the margin of error E that corresponds to the above statistics and confidence level.

8)____________

9) Use the sample data and confidence level to construct a confidence interval estimate of the population mean μ.

9)____________

10) Find the minimum sample size required to estimate a population mean μ.

10)___________

Margin of error: 5 seconds; confidence level: 95%; σ = 20 seconds.

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11) The following is a 95% confidence interval of the proportion of female medical school students: 0.449 < p < 0.511, based on data from the American Medical Association. What is the best point estimate of the proportion of females in the population of medical school students? Write a brief statement that correctly interprets the confidence interval given.

11)___________

12) In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages and 64% of them said that they did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic beverages.

12)___________

13) Based on the confidence interval you constructed in question 13, can we safely conclude that the majority of adults consume alcoholic beverages? Explain your reasoning.

13)___________

14) Find the critical value tα / 2 that corresponds to the given confidence level.

90%; n = 25; σ is unknown; population appears to be normally distributed.

14)___________

15) Use the following confidence level interval limits to find the point estimate x and the margin of error E. Biologists, studying the weights of mountain whitefish, in grams, find the confidence interval of the mean weights from 328.1 to 713.5 actually does contain the true value of μ.

15)___________

For the next two questions, assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Medical researchers studying cochlear implants, devices placed behind the bone in the ear to improve hearing, found the following number of implants over the last twelve years in children under 3 years old. Use a 90% confidence level and the following sample data: 40 90 99 120 150 220 300 320 460 520 600 650 16) Find the margin of error E that corresponds to the above statistics and confidence level.

16)___________

17) Use the sample data and confidence level to construct a confidence interval estimate of the population mean μ.

17)___________

For the next two questions, assume that a simple random sample has been taken and the population is normally distributed. Ornithologists studying the quality of weight gain in the Fall for the Screech Owl determined that the standard deviation of the weight gain of a sample of 10 screech owls was 11.97 grams. Use a 95% confidence level.

18) Find the critical value χ L2 .

18)___________

19) Use the sample data and confidence level to construct a confidence interval estimate of the L population standard deviation σ .

19)___________

20) Draw a diagram of the chi-square distribution. Discuss its shape and values.

20)___________

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Answer Key Testname: CHAPTER 7 EXAM C 1) zα / 2 = ±1.65 2) The sample must be a simple random sample and there is a loose requirement that the sample values appear to be from a normally distributed population.

3) pˆ = .211; E = .017 4) E = 0.0418 5) (0.0584, 0.142) 6) n = 263 7) x = 15; E = 1.04 8) E = 411 9) (9089, 9911) 10) n = 62 11) Best point estimate of proportion: 0.480. We have 95% confidence that the limits of 0.449 and 0.511 contain the true value of the proportion of females in the population of medical school students.

12) 61.5% < p < 66.5%.

13) Because the entire confidence interval is above 50%, we can safely conclude that the majority of adults consume alcoholic beverages (although a one-sided claim would be analyzed differently).

14) tα /2 = ±1.711 15) x = 520.8; E = 192.7 16) E = 110.6 17) (186.9, 408) 18) χ L2 = 2.7 19) (8.21, 21.85) 20) Answers may vary. The chi-square distribution is non-symmetric and skewed to the right. The values are 0 and positive. The chi-square distribution is different for each number of degrees of freedom.

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